Abstract
We study the asymptotic behaviors of the colored Jones polynomials of torus knots. Contrary to the works by R. Kashaev, O. Tirkkonen, Y. Yokota, and the author, they do not seem to give the volumes or the Chern-Simons invariants of the three-manifolds obtained by Dehn surgeries. On the other hand it is proved that in some cases the limits give the inverse of the Alexander polynomial.
| Original language | English |
|---|---|
| Pages (from-to) | 547-555 |
| Number of pages | 9 |
| Journal | International Journal of Mathematics |
| Volume | 15 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2004 Aug |
| Externally published | Yes |
Keywords
- Alexander polynomial
- Colored jones polynomial
- Torus knot
- Volume conjecture
ASJC Scopus subject areas
- Mathematics(all)